A Project Has the Activity Duration and Cost Information Indicated

question 67

Essay

A project has the activity duration and cost information indicated in the table where all times are in weeks.What is the lowest total cost for completing this project in 33 weeks?
$$\begin{array} { | l | l | l | l | l | l| } \hline \text { Activity } & \begin{array} { l } \text { Narmal } \\\text { time }\end{array} & \begin{array} { l } \text { Crash } \\\text { time }\end{array} & \begin{array} { l } \text { Normal } \\\text { Cost }\end{array} & \begin{array} { l } \text { Crash } \\\text { Cost }\end{array} & \text { Predecessor } \\\hline \text { A } & 8 & 5 & \$ , 000 & 2,000 & \\\hline B & 6 & 4 & 1,500 & 2,000 & \text { A } \\\hline \mathrm { C } & 8 & 5 & 1,800 & 2,300 & \text { A } \\\hline \mathrm { B } & 12 & 9 & 1,000 & 1,800 & \mathrm {~B} \\\hline \mathrm { E } & 14 & 11 & 950 & 1,450 & \mathrm {~B} \\\hline \mathrm { F } & 9 & 7 & 1,500 & 1,900 & \mathrm { C } , \mathrm { D } \\\hline \mathrm { G } & 7 & 5 & 2,300 & 2,800 & \mathrm { E } , \mathrm { F } \\\hline\end{array}$$

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Definitions:

Probability

A measure of the likelihood that an event will occur, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Independent Events

Two or more events where the occurrence or outcome of one event does not affect the occurrence or outcome of the other.

P(A And B)

The probability of both event A and event B occurring together.

P(A Or B)

The probability that either event A or event B occurs or both events occur together, a fundamental concept in probability theory.